{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WOAXJPJUPVBXO4N6PTOWTKLBXS","short_pith_number":"pith:WOAXJPJU","schema_version":"1.0","canonical_sha256":"b38174bd347d437771be7cdd69a961bc9e6e3db56fcadd44007f65c2f51cdc30","source":{"kind":"arxiv","id":"1808.05750","version":1},"attestation_state":"computed","paper":{"title":"Complete Test Sets And Their Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Eugene Goldberg","submitted_at":"2018-08-16T05:12:06Z","abstract_excerpt":"We use testing to check if a combinational circuit $N$ always evaluates to 0 (written as $N \\equiv 0$). We call a set of tests proving $N \\equiv 0$ a complete test set (CTS). The conventional point of view is that to prove $N \\equiv 0$ one has to generate a trivial CTS. It consists of all $2^{|X|}$ input assignments where $X$ is the set of input variables of $N$. We use the notion of a Stable Set of Assignments (SSA) to show that one can build a non-trivial CTS consisting of less than $2^{|X|}$ tests. Given an unsatisfiable CNF formula $H(W)$, an SSA of $H$ is a set of assignments to $W$ that "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.05750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-08-16T05:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"2d93f20d85f147e1602b2872e854069cbe548cecf4b4e11d6bca3ca7a522cf2c","abstract_canon_sha256":"af37451621b390cdf6bee66ceaa52690d443c2298e1f91c01e46886f3edfa020"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:52.260500Z","signature_b64":"5ulTOcYmSa5dzBGChVANJvQv9dbz9xQXSWOY9uzDAsKRb4D3YiVFIKDndOZDd7m5vm0KnUhMk02+JDj+ZdY5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b38174bd347d437771be7cdd69a961bc9e6e3db56fcadd44007f65c2f51cdc30","last_reissued_at":"2026-05-18T00:07:52.259944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:52.259944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Test Sets And Their Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Eugene Goldberg","submitted_at":"2018-08-16T05:12:06Z","abstract_excerpt":"We use testing to check if a combinational circuit $N$ always evaluates to 0 (written as $N \\equiv 0$). We call a set of tests proving $N \\equiv 0$ a complete test set (CTS). The conventional point of view is that to prove $N \\equiv 0$ one has to generate a trivial CTS. It consists of all $2^{|X|}$ input assignments where $X$ is the set of input variables of $N$. We use the notion of a Stable Set of Assignments (SSA) to show that one can build a non-trivial CTS consisting of less than $2^{|X|}$ tests. Given an unsatisfiable CNF formula $H(W)$, an SSA of $H$ is a set of assignments to $W$ that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05750","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.05750","created_at":"2026-05-18T00:07:52.260023+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05750v1","created_at":"2026-05-18T00:07:52.260023+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05750","created_at":"2026-05-18T00:07:52.260023+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOAXJPJUPVBX","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOAXJPJUPVBXO4N6","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOAXJPJU","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS","json":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS.json","graph_json":"https://pith.science/api/pith-number/WOAXJPJUPVBXO4N6PTOWTKLBXS/graph.json","events_json":"https://pith.science/api/pith-number/WOAXJPJUPVBXO4N6PTOWTKLBXS/events.json","paper":"https://pith.science/paper/WOAXJPJU"},"agent_actions":{"view_html":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS","download_json":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS.json","view_paper":"https://pith.science/paper/WOAXJPJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05750&json=true","fetch_graph":"https://pith.science/api/pith-number/WOAXJPJUPVBXO4N6PTOWTKLBXS/graph.json","fetch_events":"https://pith.science/api/pith-number/WOAXJPJUPVBXO4N6PTOWTKLBXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS/action/storage_attestation","attest_author":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS/action/author_attestation","sign_citation":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS/action/citation_signature","submit_replication":"https://pith.science/pith/WOAXJPJUPVBXO4N6PTOWTKLBXS/action/replication_record"}},"created_at":"2026-05-18T00:07:52.260023+00:00","updated_at":"2026-05-18T00:07:52.260023+00:00"}